91影视

Let's say that the typical house has the size of A =64 m².

If we visual the simplest house model , it would have 4outdoor walls, a floor, and a roof.

Every wall will be the same length if there are walls of equal length, where

L=8m long.

We can assume the walls are 3 meters high.

So, the area of the total wall is equal to:

$$\begin{gathered} A_{\text{wall}}=4脳L脳h \\ =4脳8脳3 \\ =96{\mathrm{m}}^2 \end{gathered}$$

We can discover resistance to heat passage through the wall in the characteristics table:

$R=0.2\frac{{\mathrm{Km}}^2}{\mathrm{W}}$

The weather is cold outside, as the problem stated. Let's say the difference in temperature between outside and inside air is:

$\mathrm{螖}T=25\mathrm{C}$

energy loss through the walls is equal to:

$$\begin{gathered} {\stackrel{藱}{Q}}_w=\frac{1}{R}鈰�A_{\text{wall}} \\ 鈰�\mathrm{螖}T=\frac{1}{0.2}脳96脳25 \\ =143\frac{\mathrm{kW}}{\mathrm{h}} \end{gathered}$$

In the simple model we can say that floor and roof are the same size:

$A_{\text{roof}}=A_{\text{floor}}=64{\mathrm{m}}^2$

Calculating energy loss through the roof:

$$\begin{gathered} {\stackrel{藱}{Q}}_R=\frac{1}{R}脳A_{\text{roof}} \\ 鈰�\mathrm{螖}T=\frac{1}{0.2}脳64脳25 \\ =95.35\frac{\mathrm{kW}}{\mathrm{h}} \end{gathered}$$

Total energy loss is equal to:

$$\begin{gathered} \stackrel{藱}{Q}=143+2脳95.35 \\ =333.7\frac{\mathrm{kW}}{\mathrm{h}} \end{gathered}$$

We are given that cost is 0.007 $\frac{\mathrm{kW}}{\mathrm{h}}$.

Now let's see what is the cost for $\stackrel{藱}{Q}=333.7\frac{\mathrm{kW}}{\mathrm{h}}$:

Cost$$\begin{gathered} =333.7脳0.07 \\ =\mathrm{\$}23.4 \end{gathered}$$

If we look cost per therm of natural gas:

1 therm = 10⁵ Btu.
Now let's see what is total energy loss in terms of therm:

$\stackrel{藱}{Q}=333.7\frac{\mathrm{kW}}{\mathrm{h}}=1.14鈰�{10}^7\mathrm{Btu}=203\text{therms}$

The cost of natural gas per therm is presented to us in the problem as

1 therm = 50 cents

Calculating the cost of natural gas:

Cost$$\begin{gathered} =203脳0.5 \\ =\mathrm{\$}101.5 \end{gathered}$$

Therefore,

Cost = $101.5